Here's the thing. Pegg's explanation is not canonical until it gets into a movie.
As I've pointed out before, the explanation apparently originated with the Okudas in their new
Encyclopedia. We've seen an image of text from the book that conveys that theory, and given the lead time for publishing books, that text must've been written last year sometime. It must've been Mike & Denise Okuda who came up with the explanation to explain the discrepancies in the first two movies, and Pegg must have seen an advance copy of the
Encyclopedia, or talked about it with the Okudas at some point, and passed the idea along when it came up in an interview.
It also is very inconsistent with the rules of time travel, as established in canon.
Bull. Take it from the guy who literally wrote the book on Trek time travel -- there have
never, ever, ever been any remotely consistent "rules of time travel" in Trek canon. There's just a bunch of arbitrary handwaves that writers have made up to serve whatever story they wanted to tell at the moment. That's why I wrote the first DTI book to begin with -- in hopes of somehow taking all that disparate nonsense and creating the illusion that it could fit together in some coherent way. There's nothing about the Okudas' theory here that's any more absurd than the time loops in "We'll Always Have Paris" or the incoherent nonsense of "anti-time" in "All Good Things..." or the total mess of the Temporal Cold War.
On top of that, Star Trek Beyond falls apart, since the backstory depends on us recalling specific events from the ENT TV show, meaning that stuff has to be the same before.
First off, it doesn't depend on us recalling
anything, since it explains everything that's relevant to the film, and aside from the general historical background, it's all completely original to the movie anyway. All we need to know is that there used to be a military organization called MACOs that was folded into Starfleet when the Federation was founded, and that's clearly stated in dialogue. You could follow the story perfectly well even if you'd never seen
Enterprise.
Second, the Okudas' model doesn't require that
everything be different; it just allows for the possibility that certain things
can be. I mean, obviously if two different timelines have Kirk and Spock and the Federation in them at all, then a lot of things must have gone the same way even if other things were changed.
(And look at it this way. Pegg basically said that the '09 and Into Darkness's author's time travel model -- which also had its problems -- was wrong. If their statements have no weight, neither does Pegg's.)
Again, not Pegg's model. The Okudas came up with it first. And their model actually makes
more sense of '09 and STID, because it explains the discrepancies that didn't fit the original model, like the
Kelvin's unusual size, Pike being a decade too old, and Earth's cities being far more built up. I suspect that's why the Okudas came up with the model in the first place -- because they didn't find the existing explanation adequate to reconcile the differences. The irony is that
Beyond is the one Bad Robot movie that
doesn't need the new theory, because it's much easier to reconcile with pre-2233 canon.